P h e n o m e n o lo g y o f L ittle st H ig g s M o d e l …research.ipmu.jp/seminars/focusweek07/Dec19/yuan.pdfP h e n o m e n o lo g y o f L ittle st H ig g s M o d e l w ith T-

C.-P. Yuan (MSU) Phenomenology of LHT 1

Phenomenology of Littlest Higgs Model with T-parity

C.-P. Yuan

Phys. Lett. B640, 263 (2006)Phys. Rev. D74, 115020 (2006)Phys. Rev. D76, 075007 (2007)hep-ph/0612243

In collaboration with Sasha Belyaev, Qing-Hong Cao,Chuan-Ren Chen and Kazuhiro Tobe

(Based on the talk given by Chuan-Ren Chen atArgonne National Laboratory, 12/12/07)


Little Hierarchy ProblemLittlest Higgs Model with T-parity

Summary

Outline

Motivation and Model

Higgs Physics in the LHT

Production and Decay of new particles at the LHC

Searching for the T-odd gauge boson at the LHC and LC

Top Physics in the LHT


Effective SM Little Hierarchy Problem

Electroweak precision measurements prefer a light Higgs boson!

"!182#$% @95% C.L.

"!&

2 # $'(

2

16%2&2 # $'100#$% (

2

& # 1)$%


Little Hierarchy Problem Effective SM

NO new physics is needed up to ~5 TeV

Summary tension between 1 TeV and 5 TeV !!

Schmaltz et al, hep-ph/0502182, and references therein

broken symmetry operators scale ! (TeV)B, Lflavor (1&2), CPflavor (2&3)

Custodial SU(2)non (S-parameter)

'QQQL ( )&2

' *d s *d s ( )&2

mb '*s+,-F,-b ( )&2

'h†D,h (2) &2

'D2h†D2h ( )&2

1013

1000

50

5

5

(fine-tunning)


Little Hierarchy Problemsolution: cancellation of quadratic divergences

New

&2 Canceled !! at least, at one-loop level

"!&

2 # $ 116%2

!*$+

2 ln &2

!*$+

2

!*$+

# 1)$% "!&

2 # $'100#$% (2

e.g. Supersymmetry, Little Higgs models


Littlest Higgs model with T-parity Little Higgs mechanism (collective symmetry breaking )

"mh2 # $.1

2.22

16%2f 2 ln &2

f 2

.1/0 or .2/0 "mh2 0 0

Higgs is a pseudo-Nambu-Goldstone boson

Higgs mass is protected by two independent symmetries, i. e., Higgs is massless unless two or more couplings exist simultaneously (collective symmetry breaking)L / .1 L 11.2 L 2

if .1 # .2 # 1, f /1 TeV , & # 4% f"mh2 # $O '100GeV (2

Arkani-Hamed, Cohen, Georgi, hep-ph/0105239

Georgi, Pais

The quadratic divergences are canceled by the particles with the same spin statistics


Littlest Higgs model with T-parity Littlest Higgs model

SU(5) / SO(5) non-linear sigma model

[SU(2) x U(1)]2 SU(2) x U(1)

2/exp32i4f 520

4/67282 h 9282

h† : hT

9282† h* 7282

T ;585

20/61282

11282

;585

SU(5) SO(5)

The Higgs boson is an exact GB under both SU(3)1 and SU(3)2

VEV

at scale f

GB fields

Arkani-Hamed, Cohen, Katz, Nelson hep-ph/0206021

Global Gauged


Littlest Higgs model with T-parity Littlest Higgs model

Mixing between the SM gauge bosons and heavy gauge bosons < parameter ! 1 at tree level

f = 4 TeV

W W’ W

<h> <h> <h><h>

Csaki, Hubisz, Kribs, Meade and Terning, hep-ph/0211124Hewett, Petriello and Rizzo, hep-ph/0212228

Chen, Dawson, hep-ph/0311932

Contribute significantly to EW observables

new particle ~ few TeV, need fine-tunning again


Littlest Higgs model with T-parity T-parity

A discrete symmetry

SU '2(18U '1(1 SU '2(28U '1(2

W W’ W

<h> <h> <h><h>

NO mixing between the SM gauge bosons and heavy gauge bosons (T-even) (T-odd) " parameter = 1 at tree level

f = 500 GeV Hubisz, Meade, Noble, Perelstein, hep-ph/0506042 Contributions to EW observables are loop suppressed

Dark Matter candidate Hubisz, Meade, hep-ph/0411264Asano, Matsumoto, N. Okada, Y. Okada, hep-ph/0602157Birkedal, Noble, Perelstein, Spray, hep-ph/0603077

Cheng, Low, hep-ph/0308199, hep-ph/0405243 Low, hep-ph/0409025

W W’ W

<h> <h> <h><h>

Chen, Cheung, Yuan, hep-ph/0605314Perelstein, Spray, hep-ph/0610357


Littlest Higgs model with T-parity Top sector Low, hep-ph/0409025Hubisz, Meade, hep-ph/0411264

i,j,k summed over 1,2,3x,y summed over 4,5

)

Before EWSB: mt / 0 mT +/ >.1

21.22 f

mT_ / .2 fT-evenT-odd

!"## -!

0 !$

)

$.1.2

>.121.2

2*t t h1

.12

2>.121.2

2 f*T +T+hh$

.12

>.121.2

2*t LT1Rh

$>.121.2

2 f *T +T+$.2 f *T _T _1?


Littlest Higgs model with T-parity Top sector

T-even heavy T+ contributions cancel !2

( $3.1

2.22

.121.2

2@d 4k'2%(4

1k 2

$3.1

4

.121.2

2@d 4k'2%(4

1k 2$mT +

2

3.1

2

f >.121.2

2mT +

@ d4k

'2%(41

k 2$mT +

2

(

T+

T+

Sum = 0•!2+ • • •


Littlest Higgs model with T-parity T-odd fermions

Additional T-odd fermion fields Low, hep-ph/0409025Hubisz, Meade, hep-ph/0411264

A2 / '0 ,0,0,q 2 (T

A1 / 'q 1 ,0,0, 0 (T

Ac / 'qc ,Bc ,qc (T~

LC/$C f ' *A2DAc1 *A120ED†EAc (1h.c.

D/exp 3i 4) f 5

modd />2C f

T-odd fermions are unique for the model with T-parity!

A1 $20A2 Ac $Ac D ED†ET T T

includes Higgs


Littlest Higgs model with T-parity

T-odd :

Particle spectrumW ± , Z , F , h

W H± , Z H , AH , 9

Low, hep-ph/0409025Hubisz, Meade, hep-ph/0411264

summary: Little Higgs models solve the little hierarchy problem

T-parity relaxes EWPO constrains, new particles could be light

“ heavy photon ” triplet Higgs

mu-~md

-~ >2kq f

me -~m--

~>2k l f

mWH~mZH~g f

mAH~g ' f )>5 m9~>2mh f )v

(dark matter candidate)mT -

~.2 f

mT +~>.1

21.22 f

T-even : u 3, d 3, e 3, - 3, T+ ," " " "

u - 3, d - 3, e - 3, -- 3, T - ," " " "


Littlest Higgs model with T-parity Constrains on T-odd fermions

4 fermion operators

~ $C2

128%2 f 2*f F, f *f F, f

modd ! 4.8' f1TeV (

2

TeVuniversal #

non-universal # (lepton = quark)

Cl2Cq

2

Cl2$Cq

2ln' ClCq ( !

128%3 f 2

'26.4TeV (2

Hubisz, Meade, hep-ph/0411264Hubisz, Meade, Noble, Perelstein, hep-ph/0506042

Cao, Chen, arXiv: 0707.0877[hep-ph]

modd~>2C f

O 'eedd (


Littlest Higgs model with T-parity Impacts of T-odd fermions High energy behavior of q *q 0 W H

1W H$

AF / $sw2 sinG

3f2s AZ / $'1$ 4

3sw2 ( sinG

4f 2s At / sinG

4f 2s AF1AZ1At/0

J = 1 partial wave, f = 1 TeV

Belyaev, Chen, Tobe, Yuan,hep-ph/0609179sHmWH

2

restore the unitarity

W H1

W H$

W H$

W H1


Higgs physics in the LHT Higgs search at the LHC

gluon-gluon fusion dominates !!

~ factor 5 larger than the 2nd largest one (WW fusion), when Higgs is light


Higgs physics in the LHT Contributions form new particles

cancellation of quadratic divergences

New




attach two gluons

hh hh

New

NEW




attach two gluons and one of the Higgs fields take its vev

h hNEW

New




attach two gluons and one of the Higgs fields take its vev

h h

Higgs production via gluon-gluon fusion

Chen, Tobe, Yuan, hep-ph/0602211

New

NEW



NEW

both T-even and T-odd particles will contributethe contributions from new particles in LHT will reduce the production rate via gluon-gluon fusion process

g

ghmt

g htt

top loop

AtLHTImt ghttLHT1mt2

mtHmh2

ghttLHT ~ghttSM 61$312R213R4

4 '11R2(2

v 2

f 21?;

forAtSMImt g httSM1mt2

R/.1.2




g

ghmT + g hT +T +

Heavy T-even top loop

AT +

LHTImT +g hT +T +

1mT +

2

g

ghmodd

g hf $ f$

AoddLHTImodd ghf $ f $1modd2

Heavy T-odd quark loop

ghT +T +~$mtv

R11R2

vf

ghf$f$

~$ C

2>2vf

"AT1tASM

/ $34v 2

f 2

"AoddASM

/ $14v 2

f 2

"AtotalASM

/ $34v 2

f 21$1

4v 2

f 283 / $32v 2

f 2

mT +~>.1

21.22 f

modd ~>2C f


Higgs physics in the LHT Production

"+g g 0h J +LHT 'g g 0h ( $ +SM 'g g 0h (

The production rate could be significantly suppressed !

Corrections to the Higgs boson production total cross section via gluon-gluon fusion at the LHC



Top Physics in the LHT Correction to single-top production

Shift in W-t-b coupling

t-channel single-top production

deviation from SM prediction

Cao, Li, Yuan, hep-ph/0612243


Top Physics in the LHT Correlation between the deviation in single-top production and new particle productions

If deviation in single-top production rate is large single T

+ and T_ pair rates are also large.

contours of production cross sections (fb)

Gray region:excluded

by EWPT.Hubisz, Meade,

Nobel, Perelstein hep-ph/0506042



Top Physics in the LHT Top quark polarization

Background


Signal

decaypredominately right-handedpolarized top

Right-handed top is preferred in LHT while left-handed top in SM background


Top Physics in the LHT Spin correlation of top quarks in T-odd T_ pair production

LHT SM

Cao, Chen, Li, Yuan, detailed phenomenology study in progress.

Powerful tool to kill SM backgrounds

A good probe to the symmetry breaking scale f

For the mass measurement of T-, see Meade, Reece, hep-ph/0601124; Matsumoto, Nojiri, Nomura, hep-ph/06112249.


Heavy new particles at LHC Production and decay

Lagrangian

LanHEP : generate Feynman rules for input Lagrangian

CalcHEP : calculate production cross sections and decay decay branching ratios

Numerical results

We categorize productions of all the new heavy particles and their signatures at the LHC.

http://hep.pa.msu.edu/LHT/Belyaev, Chen, Tobe, Yuan, hep-ph/0609179

Hubisz, Meade, hep-ph/0411264Freitas, Wyler, hep-ph/0609103



C/1!

&/120

," - '. (

") + )$

/'0 ($ 9

0.15 0.65 1.4 1 1.4 0.69 (TeV)GeV

f = 1 TeV

Heavy particle decay branching ratios123(456$ 7$52'8!90$ :;8<=>123(456$7$52'8!90$ :;8<=>

?@ ?A

BC B@

DE? ?EB

?C ?A

BA AF

?E? DEA

G? @CC

AA @CC

AC @CC

@A @CC

@CC @CC

/$

H$

0$

($

."

1 0-

"/

,"/

."

$ (-

"H

,"H

."

$ /-

"0

,"0

."

1 H-

"(

,"(

T+

.1 H- (

,")$

& (

)$

."

1

-"

91

909I

,"(

,".1

,"&

,".1

,"-,

"&



)J9008K/23L8I390/5(49*M<@M(82*08A*08N$*$32(49*>

signatures:a gauge boson pair + ET + jets :LSL + ET +jets , OSL + ET +jets , 1L + ET +jets

a gauge boson + Higgs + ET + jets:1L +Higgs + ET + jet,Higgs + ET + jets,

Higgs pair + ET + jets

'q -0ZHq , ZH0h AH (

Carena, Hubisz, Perelstein, Verdier, hep-ph/0610156Belyaev, Chen, Tobe, Yuan, hep-ph/0609179



3rd generation heavy quarks signatures:

a top pair + ET

Single Heavy T-even T+

A top pair + Z-boson and Higgs



Boson-quark associated production

* gauge boson pair + jets + ET

* a Higgs + a gauge boson +jets + ET

*a Higgs pair + 1 Jet + ET

* a gauge boson + 1 Jet + ET

* a Higgs + 1 Jet + ET

signatures:



Boson pair production

Signatures:* a gauge boson + a Higgs boson +

* a gauge boson pair + ET

ET


T-odd W-boson Production and Decay

Cao, Chen, arXiv: 0707.0877[hep-ph]Production of ."."

Decay of ."

O,"

K0.156PO

."K0.653P

OQ$ K1.414C

6P

OK$ K1.414C

KP


T-odd W-boson Signature at the LHC

II0."."0,". '0$-$(,". '0,-,(

II0."."0-$R$'0$," (-,O$'0,," (

Backgrounds: II 0.. S..- S(*( S. (

C6/0.5

C6/0.3

$ , 1 R)T Signature


T-odd W-boson Kinematics

P/700#$%CK/1

d +dpT

d +dE

d +dE T

d +d :

d +dm

d +dcos G


T-odd W-boson Kinematics after cuts

I)

$ L20#$% S I)

, L20 #$% S M :$ M N2.0, M :, M N2.0R ) L175#$% S cosG$,N0.6

cuts :

O."LO

Q$

O."NO

Q$d +dpT

d +dE


T-odd W-boson Discovery potential at the LHC

U )>: contour

I)

$ L20#$% S I)

, L20 #$% S M :$ M N2.0, M :, M N2.0R ) L175#$% S cosG$,N0.6

cuts :


T-odd W-boson From the LHC to LC

LHC : di-lepton + Has a great discovery potential !!

BUT ... Can NOT determine masses of and Can NOT reconstruct kinematics of Can NOT measure the spin of

LHC :

With 4 jets + signature

R)

R)

."

."

,"

$1$$ 0.".

"0,

". '0 V V (,

". '0 V V (

,"

Can NOT determine masses of and Can NOT reconstruct kinematics of Can NOT measure the spin of

."

."

,"

,"


T-odd W-boson Production at LC

> s/1TeV mWH~g f m- _ ~>2Cl f

e-

e+

e-

e+

-_


T-odd W-boson Searching at the LC

$1$$ 0.".

"0,

". '0 V V (,

". '0 V V (

$1$$ 0-..0-*- V V V V '~ 5.6 PH (Intrinsic background :

4 V$(M1R)

Signature


V

V

V

V

T-odd W-boson reconstruction of W-boson at LC

Require :

I)

V=15#$% S M:M!3.0 S O;L0.5

Reconstruct W boson

* order 4 jets with respect to their transverse momentum I)

V1 LI)

V 2 LI)

V3 LI)

V4

* also require OWX 'O/>'!1 ' VV ($!.(

21'!2 ' VV ($!

.(

2(

* identify Ws : . 1J!' V 1 V Y( , the other one is . 2

> 99 % accuracy


T-odd W-boson Reconstruction of masses of W

H and A

H

At the rest frame of

R+

3$M/!

."

2 $!,"

2 1!+

2

2m."

I+

3$M/>6!."

2 $'!,"

1!+(2;6!

."

2 $'!,"

$!+(2;

2m."

RP /F'R+

3$MPQI+

3$M( Q/>1$!

."

2

M

O."

/> M2 >R1R$

R11R$ >11!

+

2

R1R$

1>'1$!+

2

R12('1$

!+

2

R$2(

O,"

/O.">1$2

'R11R$(

>M1

!+

2

O."

2

Kong, Park, hep-ph/0703057

(+ : max. : min.)

W H

(Similar technique has been widely used in SUSY analysis.)


T-odd W-boson Reconstruction of masses of W

H and A

H

O."

/> M2 >R1R$

R11R$ >11!+

2

R1R$

1>'1$!+

2

R12 ('1$

!+

2

R$2 ( O,"

/O." >1$2'R11R$(

>M1

!+

2

O."

2

R1 T

W AH

R$ T

RI."

Q2H

WH

AH W

RI."

Q2H

WH

d +dE w


T-odd W-boson Effects of detector effects

R1/345#$% SR$/130#$% R1/355#$% SR$/130#$%smeared

'O."

SO,"

(K'435S126(#$%

(3/$ '450S101(#$%

K'432S109(#$%

OR

R/

0.5>R

'O."

SO,"

(

" K 4% , 8%

Reconstruct the mass of ."

d +dE w

d +dE w


T-odd W-boson Reconstruction of kinematics

K. Hagiwara, R. D. Peccei and D. Zeppenfeld, Nucl.Phys.B282:253,1987.

On shell condition Momentum conservationKnown C.M. energy

reconstruct the momentum of ,

"

Probing the Weak Boson Sector in e1e$ 0 W1W $

reconstruct the momentum of W H

boost back to the rest frame of W H

Study spin of W H


T-odd W-boson Reconstruction of kinematics

Hagiwara, Peccei, Zeppenfeld, Nucl.Phys.B282:253,1987. e1e$0AA'0B'C '

S BC

2 Rp B TRp C/EA2$mA2 $'EB2$mb2 ($'EC2 $mC2 ( ,

p e -/'Et , 0, 0, $Et (pe1/'Et , 0, 0, Et (EA/EB1EC , EA'/EB'1EC '

mA/mA' , mB/mB' , mC/mC'

Rp A/Rp B1Rp C , Rp A'/Rp B'1Rp C ' ,

Rp B1Rp C1Rp B'1Rp C'/0

2 Rp B' TRp C/'Ec '2 $mc '2 ($'EA2$mA2 ($'EB2$EB'2 ($2 Rp B TRp B'

2 Rp B TRp C/EA2$mA2 $'EB2$mb2 ($'EC2$mC2 (

pC2 /EC2 $mC2

Rp C/URp B1QRp B'1FRp B8Rp B'


T-odd W-boson Spin of ."

."

GV

W

AH

WH P-wave dominates

rest frame of

true~sin2

G*

spin-1 to 2 scalars

d +dE w

d +dcos G*


T-odd W-boson Spin of ."

."

GV

W

AH

WH

rest frame of

After reconstruction

d +dcos G*

d +dE w


T-odd W-boson Distinguishing different models

GV

W

Y

X

LHTscalarfermionfermion

d +dcos G*

d +dcos G*

d +dcos G*


Summary

Little Higgs mechanism provides a solution for solving the “ little hierarchy ” problem.

T-parity forbids the mixing btw the SM and heavy gauge bosonsavoiding EWPT, lowering f, LHC could copiously produce new particles.

The Higgs boson production rate via gluon fusion is suppressed.

The LHC has a great potential to discover the signatures of new particles ( WH ) predicted in the LHT.

The physics quantities (mass, spin) could be measured at the LC, different models could be distinguished.

Polarization states of top quarks could provide the evidence of LHT.

Documents

P h e n o m e n o lo g y o f L ittle st H ig g s M o d e l …research.ipmu.jp/seminars/focusweek07/Dec19/yuan.pdfP h e n o m e n o lo g y o f L ittle st H ig g s M o d e l w ith T-